Métodos Hamiltonian Monte Carlo para la estimación de modelos de series climáticas

Camón Fernández, Alejandro
Asín Lafuente, Jesús (dir.)

Universidad de Zaragoza, CIEN, 2022
Departamento de Métodos Estadísticos, Área de Estadística e Investigación Operativa

Graduado en Matemáticas

Resumen: This work presents a detailed explanation of the HMC algorithm used for bayesian inference and an application to estimate, in the bayesian framework, a new proposed autoregressive model for the maximum daily temperatures.
The proposed model is based on the previous work of Castillo-Mateo et al. (2022), where the time structure of mean was modeled. A more flexible estructure is considered modeling also the variance and including interaction terms to reflect a seasonal variability of trend and persistence. The model has easily interpretable terms, it is able to represent the short and long-term dynamics of the temperatures, specially in relation to the effect of a possible climate change. Also a procedure of selection of covariates is designed and all the estimation process is implemented using RStan library, in the R workspace.
Models are fitted to series in a database built with data obtained by 18 stations placed in Aragón and its surroundings during a period of over 60 years. The estimation with the HMC-NUTS algorithm is possible but computationally slow. The results show progress towards a more complete model, because both, a non-constant variance and the addition of seasonal-trend and seasonal-persistence interactions, are necessary in Aragón series.

Tipo de Trabajo Académico: Trabajo Fin de Grado